George Walford: The Price of Precision

Exact science is able to be exact only by excluding inexactitude. In Euclidean geometry (paradigmatic of exact science) a proposition will begin: “Let ABC be a triangle… ” This establishes that what follows relates only to figures which are, exactly and without qualifications, triangles, figures bounded each of them by three lines (possessing length but not width) which are, exactly and without qualifications, straight. Figures which do not meet these requirements, being not exactly and without qualification triangles, are excluded from consideration.

If any triangle which is more than an ideal construct, any triangle which has been drawn, be examined under a microscope, it will be seen to be bounded not by straight lines but by hazy blurs of considerable width and with indefinite edges. The straight line is an illusion produced by the grossness of our senses, it is not materially present and accordingly there is no material triangle present, no material object to which the Euclidean proposition relates.

Similar reasoning applies to the propositions of the exact sciences other than Euclidean geometry. If the science is exact then it deals with objects precisely defined, and no material object over complies, exactly and without qualification, with a precise definition. The material world, commonly thought to be the special domain of exact science, is precisely what exact science can never comprehend.

from Ideological Commentary 10, January 1982.